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A proton; traveling with a velocity of 4.1 x 106 , m/s due east, experiences magnetic force that has a maximum magnitude of 6.7 x 10-14 Nand direction of due south ...

Question

A proton; traveling with a velocity of 4.1 x 106 , m/s due east, experiences magnetic force that has a maximum magnitude of 6.7 x 10-14 Nand direction of due south What are the magnitude and direction of the magnetic field causing the force? If the field is Up, then enter a number greater than zero If the field is down; then enter number less than zero:NumberUnits

A proton; traveling with a velocity of 4.1 x 106 , m/s due east, experiences magnetic force that has a maximum magnitude of 6.7 x 10-14 Nand direction of due south What are the magnitude and direction of the magnetic field causing the force? If the field is Up, then enter a number greater than zero If the field is down; then enter number less than zero: Number Units



Answers

(a) A proton, traveling with a velocity of $4.5 \times 10^{6} \mathrm{m} / \mathrm{s}$ due east, experiences a magnetic force that has a maximum magnitude of $8.0 \times 10^{-14} \mathrm{N}$ and a direction of due south. What are the magnitude and direction of the magnetic field causing the force? (b) Repeat part (a) assuming the proton is replaced by an electron.

All right, let's start with writing down everything that we know. We know the velocity me is 4.5 times 10 to the sixth. That's in meters per second. They are given the force produced by the magnetic field so abbreviate that have sabih that is equal to 8.0 times 10 to the minus 14. Now our force, as usual, is in Newton's. So were given that this is a traveling proton going at the speed. It's another thing will want. A note is the charge of a proton is 1.6 times, then B minus 19th power that is in cool unit of charge. It is the charge of a proton, so electrons and protons share the same charge. Point of note. Electrons Air Just opposite Lee directed opposite Lee charged. Now the equation we're gonna want to use to find the magnetic field it's given by B is equal to divided by the charge multiplied by he sign of the angle between the velocity and the force. They were given in this problem that the velocity is traveling east and the force is directed south. So it's right. So we have our velocity and Of course, these are 90 degrees to each other. So we have sign of 90 degrees or sign of pile for two, which is equal to one. So we don't need to keep that in this equation. No, this is a straight up plug and chug. Um, we have everything we need to calculate it, but we need to find out the direction so you can find this from using the right hand rule. If you hold your right hand palm upwards out in front of you, point you some out to the side, point your pointer finger directly forward, and then your middle finger will point up in the direction your palm is facing. They should all be at right angles to each other all perpendicular. So your pointer finger is the direction of the Byfield. Your thumb is in the direction of the velocity, and your middle finger will be the force. So if we or intake orientate our right hand in the direction we're given. So we have velocity to the east or to the right. Then we had the forces south. So you feel you'll have the bend your right hand around your middle finger or your palm is facing downwards and your thumb is pointing to the right. That should leave your pointer finger facing directly at your your faith or your chest, depending on how you're able to angle your hand for that. But for this diagram, this is a three dimensional. Um, this is a three dimensional problem, but we only have two dimensions here, So this is going to be coming out of the page. Um, which is represented by a circle with a DOT, whereas into the page is represented by an ax inside of the city. This is out of the pages in. Okay, so now we have direction squared away. Weaken, calculate this out. Plugging in all of this gives you that be, is what we're solving for. The magnetic field is equal to 0.1 one. So we have a number. Let's make sure it's what we want by double checking with their units. So F is in units of Newton's que is in units of cools See And now he is in units meters per second. So it's cool moms times meter for a second. If you wanted to help you see the next appear low but easier. You can put the Coolum in the numerator here just time. Cool, sometimes meter divided by second. So but want to do is move this second up to the numerator. We can do that. You can see it a little easier if you just read it in seconds over one to move it up. You just flip it. So this isn't this denominator here. So we we flip it so it would be seconds over one multiplied by that. So what we're left with is Newton time second over, cooling times, meter for meter times. Cool. Which is the definition of the Tesla, which is our units for magnetic field. The abbreviated as a t. You know, we have a final answer be is equal to zero point point 11 test now to find what what happened with an electron? As I said earlier, electron in protons have the same charge. That wouldn't affect any of the numbers. Uh, for the proton, it's directed out of the page, as we discovered with the right hand roll with a negative charge. You do that opposite of what you find with her again rule to make things even more confusing. So we found that this points out of the page with an electron. It's just imagine your middle finger pointing in the opposite direction is actually pointing, So we'll be pointing into the page, which is the opposite of what we found for the proton. So for part B, we have an electron that would be in the page, same number, and there you have it.

So we have a proton that is traveling at an angle 37 west of north. A magnetic field is pointing to the north, and we need to determine for part a the magnitude of the magnetic force on the proton, for part being the direction of the magnetic force. And for part C, the protons acceleration as it moves through the magnetic field. So let us recall that the formula for a magnetic force is the charge times of velocity times the magnetic field. But it is also times sine of the angle, and so here were given. The charge is 1.60 times 10 to the negative 19 cool ums. The velocity is 3.0 times 10 to the sixth meters per second. The magnetic field is 0.30 Tesla and the angle fada is equal Thio 37 degrees since it is west of north. So plugging these values into the equation, you will get that the force is equal to 8.7 times 10 to the negative 14 Newton's Okay, so let's look at part C and then we will look at part B, so Part C wants us to find the acceleration. So let's remember that force is also equal to mass times the acceleration. So the acceleration is equal to the force divided by the mass. We just found the force in part A and the mass is equal to 1.673 times 10 to the negative 27 kilograms. Therefore, the acceleration is equal to 5.2 times 10 to the 13th meters per second squared and looking at part B. So the magnetic field is north. The velocity is in the northwest direction. So using the right hand rule, the force on the proton is perpendicular to the northwest plane.

All right. So let's consider a situation where we have a magnetic field pointing to the north. And within that magnetic field we have a proton that is moving at an angle do bad era, where that angle here between the field and the protons path is 37 degrees, 37 degrees. So we want to find a few things out about this. First, we want to know what the force on the Proton iss. We don't know the direction, and we also want to know the acceleration. So first thing we can do is start with the force. Our magnetic force equation that would be, by the way be is equal to charge of the particle velocity of the particle strength of the magnetic field times the sine of the angle between them, which in this case, we're gonna be 37 degrees. All you gotta do is plug all that into your calculator and your force you should get is gonna be 8.67 times 10 to the negative 14 Newtons. Now, to figure out our direction that the force is gonna be in, we use the right hand rule. So take your fingers and point them in the direction that the red arrow is pointing. And then you're gonna curl your fingers towards the Blue Arrow, and we always know that the force has to be perpendicular to both the velocity and to the magnetic field. So in this case, the force is going to go straight into the page, so force, and so that is this much force into the page. And then finally, we want to find our acceleration, which using the F equals m A. We just rearranged a little bit and you get a equals. The force divided by the mass, the mass of a proton is easily found. And so if you divide your 8.67 times 10 to the negative 14 by the mass, which is 1.673 times 10 to the negative 27 you should get an acceleration of five point 182 times tend to the 13 meters per second squared. And so these are your three answers the force, the direction and the acceleration

This problem covers the concept of the motion of a charge in a magnetic field. The production is moving along the west direction and the magnetic field of the earth is oriented along the vote downward direction. So first we need to solve for the direction of the magnetic force on the platoon. And by using right hand come rule regard the direction of the fools is along the southward direction. So this is the direction of the force magnetic force under uh on your phone along this our direction. And the magnitude of the force Securing the charge on the protein that is 1.6 into. And this -19 columns dan six speed. And that is 6.2. And to remember six m 4 seconds okay into uh the strength of the magnetic feed that is 50 In to tenders -6 Tesla. And since the Angle between the speed angle between the velocity and the magnetic field is 90°, we can That killed 70 days. So the magnitude of the force is it cuba into 4.96 into tenders -17 Newton's. And if we predict the direction that we have predicted by using the right hand rule so we can see the magnetic force is acted along south direction


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